Question

Yasmin has a bag containing 165 colored beads. Her classmates take turns selecting one bead without looking, recording the color in the table, and replacing the bead. if the bag contained an equal amount of each color of bead, for which color is the experimental probability closest to the theoretical probability?

Red- 10- 30
Brown- 15- 45
Orange- 17- 51
Yellow-13- 39

Answer 1

orange

Explanation:

If the bag contained an equal amount of each color of bead, we would expect each color to have 1/4 or 25% of the total number of beads, which is 165. Therefore, the theoretical probability of selecting a bead of each color would be 25%.

To determine which color has the experimental probability closest to the theoretical probability, we can compare the experimental probability of selecting a bead of each color to the theoretical probability of 25%. We can use the following formula to calculate the experimental probability:

experimental probability = number of times color is selected / total number of selections

The results are:

Red: 10/165 = 0.061 or 6.1%

Brown: 15/165 = 0.091 or 9.1%

Orange: 17/165 = 0.103 or 10.3%

Yellow: 13/165 = 0.079 or 7.9%

To find the color with the experimental probability closest to the theoretical probability of 25%, we can calculate the difference between the experimental probability and the theoretical probability for each color:

Red: 25% - 6.1% = 18.9%

Brown: 25% - 9.1% = 15.9%

Orange: 25% - 10.3% = 14.7%

Yellow: 25% - 7.9% = 17.1%

Based on these calculations, the color with the experimental probability closest to the theoretical probability is orange, with a difference of 14.7%. Therefore, orange is the color for which the experimental probability is closest to the theoretical probability of selecting a bead of each color.